I am not sure if the reconstruction is done automagically in software-raid. All I know is that after your replace the defective HDD, you have to do something like this (depending on what drive you have, e.g. sdx for SATA):

Also, if you have partitions in your drive, maybe you should create them with fdisk before you run the above command.

If you need perfect Linux compatibility and good performance, after A LOT OF SEARCH I found out that if you are on a tight budget host-based SATA RAID controllers with Silicon Image 3114 chipset is the way to go, and if money is not an issue full-hardware controllers like LSI Logic MegaRAID SATA 150-4 (4 channels) or LSI Logic MegaRAID SATA 150-6 (6 channels) is the best option.

How do you setup the system to notify you with email in case of a drive failure?